Mind that every X PERIOD, is absolute, if you started your server at 10:44 pm and set to every 1 h, it will be executed at 11:44pm, 0:44am and so on...
You can have your cron executed at the next plain hour and every next hour then.

Use every plain hour for that. (eg:If started at 3:46, next exec will be 4:00 then 5:00...)
Same can be done with minutes with every plain minute (eg: Started at 3:46, next exec will be 3:50,4:00,..)

Next :

Parse : every PERIOD on the ORDINALNUMBER PERIOD of the PERIOD
eg : every minutes on the first day of the month

Parse : every ORDINALNUMBER PERIOD of PERIOD
eg: every first day of the month

~~Handle 24-hour times (at 01:00 will be 01:00am, at 16:00 will be 4:00pm) : ~~ DONE

Handle days

handle months

Handle years

About you

If this can help even one person, I would be hapi enough (see what I did here ? :D).
I will work on that project till I will be confident enought that it will answer perfectly to the need to at least one person.
If you are that person, please, do not hesitate to :

I would like to have any feedback that you use it, may be even for what and how I could help improving this package to fit your needs.

About stuff

Limitations :

About max_time : For now (till I get smart and find a way to handle that), you can't plan something over 68 years.
I was stuck at 24 days initially (INT 32 limit on setTimeout), but I excess that limit by forcing me to work in seconds instead of milliseconds.
I will, probably, I think, may be, move that limit away.
But for now, if you want to code an IA that plan to nuke the world in 69 years. Mind about setting up to 67/68 years instead.

Versioning

Releases will be numbered with the following format (semver):

<major>.<minor>.<patch>

The reason we doing that, is that, far from marketing or stuff. You will know easily if a breaking change occurs by
just looking the first number. Mind that some major version (breaking changes) can be absolutely necessary (bugfix).
But at least it won't break your code